VORTICAL FLOW OUTSIDE A SPHERE AND SOUND GENERATION

Formulas are presented for an incompressible inviscid velocity field V with a vorticity field hi outside of a rigid sphere and for the far-f ield sound generation. The velocity V is expressed as the sum of an im age velocity v and a known velocity v in R-3, which is induced by the same vorticity field Omega outside the sphere and the extension Omega = 0 inside. We derive formulas for the image velocity v and the corr esponding image potential Phi, which in turn yields the far-field sou nd. These formulas are applied to define the velocity of a slender vor tex filament in the presence of a rigid sphere and the associated far- field sound.